SEM
Data relationships revisited
I tried transforming the data because we are running linear regressions. Some of the data might result in non-normal residuals by the nature of their data. So I applied log transformations to data that seemed related to count values or seemed log-normal (trees within 10m, density of coffee, distance to nearest tree, and wind). I applied an arcsin square-root transformation for proportion data (shade and leaves infected)
Relationships between untransformed data
chart.Correlation(roya_quadmax %>%
select(roya.max, coffeeDensity_m,
wind_m.s, shadeAvg_pc, avgTreeDist,
tree_10m, evap) %>%
as.matrix(), histogram=TRUE, pch=19)
Relationships between transformed data
chart.Correlation(roya_quadmax %>%
select(roya_asqt, coffeeDens_ln,
wind_ln, shade_asqt, treedist_ln,
tree_ln, evap) %>%
as.matrix(), histogram=TRUE, pch=19)
SEM models
I’ve gone ahead and fit the linear models to the transformed data since this meets the assumptions of the model. If we want in the future, we could fit generalized linear models that are appropriate for the original data distributions
SEM 1
m1 <- lm(roya_asqt ~ wind_ln + evap, data = roya_quadmax)
m2 <- lm(wind_ln ~ tree_ln, data = roya_quadmax)
m3 <- lm(evap ~ shade_asqt + wind_ln, data = roya_quadmax)
sem1 <- psem(m1, m2, m3)
summary(sem1, .progressBar = FALSE)##
## Structural Equation Model of sem1
##
## Call:
## roya_asqt ~ wind_ln + evap
## wind_ln ~ tree_ln
## evap ~ shade_asqt + wind_ln
##
## AIC BIC
## 45.565 76.851
##
## ---
## Tests of directed separation:
##
## Independ.Claim Test.Type DF Crit.Value P.Value
## roya_asqt ~ tree_ln + ... coef 123 1.1821 0.2395
## evap ~ tree_ln + ... coef 123 2.3836 0.0187 *
## wind_ln ~ shade_asqt + ... coef 124 -2.0960 0.0381 *
## roya_asqt ~ shade_asqt + ... coef 123 -2.0270 0.0448 *
##
## Global goodness-of-fit:
##
## Fisher's C = 23.565 with P-value = 0.003 and on 8 degrees of freedom
##
## ---
## Coefficients:
##
## Response Predictor Estimate Std.Error DF Crit.Value P.Value Std.Estimate
## roya_asqt wind_ln 0.0106 0.0328 124 0.3245 0.7461 0.0290
## roya_asqt evap 0.0072 0.0026 124 2.7341 0.0072 0.2440 **
## wind_ln tree_ln 0.1336 0.1271 125 1.0508 0.2954 0.0936
## evap shade_asqt -5.1995 3.3084 124 -1.5716 0.1186 -0.1378
## evap wind_ln 2.5591 1.0884 124 2.3511 0.0203 0.2062 *
##
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05
##
## ---
## Individual R-squared:
##
## Response method R.squared
## roya_asqt none 0.06
## wind_ln none 0.01
## evap none 0.07plot(sem1)SEM 2
n1 <- lm(roya_asqt ~ evap + tree_ln, data = roya_quadmax)
n2 <- lm(evap ~ shade_asqt + tree_ln, data = roya_quadmax)
sem2 <- psem(n1, n2)
summary(sem2, .progressBar = FALSE)##
## Structural Equation Model of sem2
##
## Call:
## roya_asqt ~ evap + tree_ln
## evap ~ shade_asqt + tree_ln
##
## AIC BIC
## 24.555 47.308
##
## ---
## Tests of directed separation:
##
## Independ.Claim Test.Type DF Crit.Value P.Value
## roya_asqt ~ shade_asqt + ... coef 123 -2.4962 0.0139 *
##
## Global goodness-of-fit:
##
## Fisher's C = 8.555 with P-value = 0.014 and on 2 degrees of freedom
##
## ---
## Coefficients:
##
## Response Predictor Estimate Std.Error DF Crit.Value P.Value Std.Estimate
## roya_asqt evap 0.0068 0.0026 124 2.6293 0.0096 0.2312 **
## roya_asqt tree_ln 0.0554 0.0461 124 1.2024 0.2315 0.1057
## evap shade_asqt -8.4275 3.3343 124 -2.5275 0.0127 -0.2234 *
## evap tree_ln 4.1492 1.5658 124 2.6499 0.0091 0.2342 **
##
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05
##
## ---
## Individual R-squared:
##
## Response method R.squared
## roya_asqt none 0.07
## evap none 0.08plot(sem2)SEM 3
o1 <- lm(roya_asqt ~ shade_asqt + tree_ln, data = roya_quadmax)
o2 <- lm(shade_asqt ~ tree_ln, data = roya_quadmax)
sem3 <- psem(o1, o2)
summary(sem3, .progressBar = FALSE)##
## Structural Equation Model of sem3
##
## Call:
## roya_asqt ~ shade_asqt + tree_ln
## shade_asqt ~ tree_ln
##
## AIC BIC
## 14.000 33.909
##
## ---
## Tests of directed separation:
##
## No independence claims present. Tests of directed separation not possible.
##
## Global goodness-of-fit:
##
## Fisher's C = 0 with P-value = 1 and on 0 degrees of freedom
##
## ---
## Coefficients:
##
## Response Predictor Estimate Std.Error DF Crit.Value P.Value Std.Estimate
## roya_asqt shade_asqt -0.2937 0.0983 124 -2.9893 0.0034 -0.2632
## roya_asqt tree_ln 0.1088 0.0461 124 2.3588 0.0199 0.2077
## shade_asqt tree_ln 0.1061 0.0409 125 2.5942 0.0106 0.2260
##
## **
## *
## *
##
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05
##
## ---
## Individual R-squared:
##
## Response method R.squared
## roya_asqt none 0.09
## shade_asqt none 0.05plot(sem3)